Voltage sensor-less position detection in an active front end

ABSTRACT

A controller may include a memory having computer-readable instructions stored therein; and a processor configured to execute the computer-readable instructions to generate Pulse Width Modulation (PWM) signals to control power switches of an Active Front End (AFE) inverter based on at least a synthesized grid voltage vector angle at a terminal of an alternating current (AC) grid without using physical voltage sensors at the terminal of the AC grid, and control the AFE inverter to supply power to a load based on the PWM signals.

BACKGROUND 1. Field

Example embodiments relate generally to an apparatus configured todetect: an angle of a grid voltage vector at a terminal of analternating current (AC) grid, a system and/or a method of performingsame.

2. Related Art

In an Active Front End (AFE) control system, a phase locked loop (PLL)based control method is often used to detect an angle of a grid voltagevector at a terminal of an alternating current (AC) based on gridline-to-line voltage information. Conventionally, in order to detect theangle of the grid voltage vector of the AC grid, the grid line-to-linevoltage information may need to be sensed first using external voltagesensors attached to terminals of the AC grid.

SUMMARY

Some example embodiments relate to a controller and/or a method ofgenerating Pulse Width Modulation (PWM) signals for power switches of anActive Front End (AFE) inverter.

In some example embodiments, the controller may include a memory havingcomputer-readable instructions stored therein; and a processorconfigured to execute the computer-readable instructions to, generatePulse Width Modulation (PWM) signals to control power switches of anActive Front End (AFE) inverter based on at least a synthesized gridvoltage vector angle at a terminal of an alternating current (AC) gridwithout using physical voltage sensors at: the terminal of the AC grid,and control the AFE inverter to supply power to a load based on the PWMsignals.

BRIEF DESCRIPTION OF THE DRAWINGS

At least some example embodiments will become more fully understood fromthe detailed description provided below and the accompanying drawings,wherein like elements are represented by like reference numerals, whichare given by way of illustration only and thus are not of exampleembodiments and wherein:

FIG. 1 is a block diagram of a system for controlling a load accordingto some example embodiments;

FIG. 2 illustrates a method of controlling a system based on voltagesensorless position detecting according to some example embodiments;

FIG. 3 illustrates a method of operating a controller to perform avoltage sensorless position detecting in a system according to someexample embodiments;

FIG. 4 illustrates a voltage sensorless position detecting moduleaccording to some example embodiments,

FIG. 5 illustrates a method of operating a voltage sensorless positiondetecting module according to some example embodiments;

FIG. 6 illustrates a method of estimating the inverter terminal voltageaccording to some example embodiments;

FIG. 7 illustrates a block diagram of an inverter terminal voltagevector angle detecting module included in a voltage sensorless positiondetecting module according to some example embodiments;

FIG. 8 illustrates a method of estimating the inverter terminal voltagevector angle according to some example embodiments;

FIG. 9 illustrates a method of estimating the grid voltage vector angleaccording to some example embodiments;

FIG. 10 illustrates a method of generating an initial terminal voltagevector angle according to some example embodiments;

FIGS. 11A to 11C are vector diagrams illustrating current and voltagevectors in a direct-quadrature (dq) rotating reference frame accordingto some example embodiments; and

FIG. 12 is a circuit diagram illustrating an AFE inverter connected to aload according to some example embodiments.

DETAILED DESCRIPTION

Some example embodiments will now be described more fully with referenceto the accompanying drawings in which some example embodiments areillustrated.

Accordingly, while example embodiments are capable of variousmodifications and alternative forms, embodiments thereof are shown byway of example in the drawings and will herein be described in detail.It should be understood, however, that there is no intent to limitexample embodiments to the particular forms disclosed, but on thecontrary, example embodiments are to cover all modifications,equivalents, and alternatives falling within the scope of the claims.Like numbers refer to like elements throughout the description of thefigures.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement, without departing from the scope of example embodiments. Asused herein, the term “and/or” includes any and all combinations of oneor more of the associated listed items.

It will be understood that when an element is referred to as being“connected” or “coupled” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected” or “directly coupled” to another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between” versus “directly between,” “adjacent” versus “directlyadjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of exampleembodiments. As used herein, the singular forms “a,” “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprises,” “comprising,” “includes” and/or “including,” when usedherein, specify the presence of stated features, integers, steps,operations, elements and/or components, but do not preclude the presenceor addition of one or more other features, integers, steps, operations,elements, components and/or groups thereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which example embodiments belong. Itwill be further understood that terms, e.g., those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Portions of example embodiments and corresponding detailed descriptionare presented in terms of software, or algorithms and symbolicrepresentations of operation on data bits within a computer memory.These descriptions and representations are the ones by which those ofordinary skill in the art effectively convey the substance of their workto others of ordinary skill in the art. An algorithm, as the term isused here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a result. The steps arethose requiring physical manipulations of physical quantities. Usually,though not necessarily, these quantities take the form of optical,electrical, or magnetic signals capable of being stored, transferred,combined, compared, and otherwise manipulated. It has proven convenientat times, principally for reasons of common usage, to refer to thesesignals as bits, values, elements, symbols, characters, terms, numbers,or the like.

In the following description, illustrative embodiments will be describedwith reference to acts and symbolic representations of operations (e.g.,in the form of flowcharts) that may be implemented as program modules orfunctional processes including routines, programs, objects, components,data structures, etc., that perform particular tasks or implementparticular abstract data types and may be implemented using existinghardware. Such existing hardware may include one or more CentralProcessing Units (CPUs), digital signal processors (DSPs),application-specific-integrated-circuits, field programmable gate arrays(FPGAs) computers or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” or “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computing device,that manipulates and transforms data represented as physical, electronicquantities within the computer system's registers and memories intoother data similarly represented as physical quantities within thecomputer system memories or registers or other such information storage,transmission or display devices.

In this application, including the definitions below, the term ‘module’or the term ‘controller’ may be replaced with the term ‘circuit.’ Theterm ‘module’ may refer to, be part of, or include processor hardware(shared, dedicated, or group) that executes code and memory hardware(shared, dedicated, or group) that stores the code executed by theprocessor hardware.

The module may include one or more interface circuits. In some examples,the interface circuits may include wired or wireless interfaces that areconnected to a local area network (LAN), the Internet, a wide areanetwork (WAN), or combinations thereof. The functionality of any givenmodule of the present disclosure may be distributed among multiplemodules that are connected via interface circuits. For example, multiplemodules may allow load balancing. In a further example, a server (alsoknown as remote, or cloud) module may accomplish some functionality onbehalf of a client module.

Further, at least one embodiment of the invention relates to anon-transitory computer-readable storage medium comprisingelectronically readable control information stored thereon, configuredin such that when the storage medium is used in a controller of amagnetic resonance device, at least one embodiment of the method iscarried out.

Even further, any of the aforementioned methods may be embodied in theform of a program. The program may be stored on a non-transitorycomputer readable medium and is adapted to perform any one of theaforementioned methods when run on a computer device (a device includinga processor). Thus, the non-transitory, tangible computer readablemedium, is adapted to store information and is adapted to interact witha data processing facility or computer device to execute the program ofany of the above mentioned embodiments and/or to perform the method ofany of the above mentioned embodiments.

The computer readable medium or storage medium may be a built-in mediuminstalled inside a computer device main body or a removable mediumarranged so that it can be separated from the computer device main body.The term computer-readable medium, as used herein, does not encompasstransitory electrical or electromagnetic signals propagating through amedium (such as on a carrier wave); the term computer-readable medium istherefore considered tangible and non-transitory. Non-limiting examplesof the non-transitory computer-readable medium include, but are notlimited to, rewriteable non-volatile memory devices (including, forexample flash memory devices, erasable programmable read-only memorydevices, or a mask read-only memory devices); volatile memory devices(including, for example static random access memory devices or a dynamicrandom access memory devices); magnetic storage media (including, forexample an analog or digital magnetic tape or a hard disk drive); andoptical storage media (including, for example a CD, a DVD, or a Blu-rayDisc). Examples of the media with a built-in rewriteable non-volatilememory, include but are not limited to memory cards; and media with abuilt-in ROM, including but not limited to ROM cassettes; etc.Furthermore, various information regarding stored images, for example,property information, may be stored in any other form, or it may beprovided in other ways.

The term code, as used above, may include software, firmware, and/ormicrocode, and may refer to programs, routines, functions, classes, datastructures, and/or objects. Shared processor hardware encompasses asingle microprocessor that executes some or all code from multiplemodules. Group processor hardware encompasses a microprocessor that, incombination with additional microprocessors, executes some or all codefrom one or more modules. References to multiple microprocessorsencompass multiple microprocessors on discrete dies, multiplemicroprocessors on a single die, multiple cores of a singlemicroprocessor, multiple threads of a single microprocessor, or acombination of the above.

Shared memory hardware encompasses a single memory device that storessome or all code from multiple modules. Group memory hardwareencompasses a memory device that, in combination with other memorydevices, stores sonic or all code from one or more modules.

The term memory hardware is a subset of the term computer-readablemedium. The term computer-readable medium, as used herein, does notencompass transitory electrical or electromagnetic signals propagatingthrough a medium (such as on a carrier wave); the term computer-readablemedium is therefore considered tangible and non-transitory. Non-limitingexamples of the non-transitory computer-readable medium include, but arenot limited to, rewriteable non-volatile memory devices (including, forexample flash memory devices, erasable programmable read-only memorydevices, or a mask read-only memory devices); volatile memory devices(including, for example static random access memory devices or a dynamicrandom access memory devices); magnetic storage media (including, forexample an analog or digital magnetic tape or a hard disk drive); andoptical storage media (including, for example a CD, a DVD, or a Blu-rayDisc). Examples of the media with a built-in rewriteable non-volatilememory, include but are not limited to memory cards; and media with abuilt-in ROM, including but not limited to ROM cassettes; etc.Furthermore, various information regarding stored images, for example,property information, may be stored in any other form, or it may beprovided in other ways.

The transmission medium may be twisted wire pairs, coaxial cable,optical fiber, or some other suitable transmission medium known to theart.

The example embodiments may have different forms and/or be combined, andshould not be construed as being limited to the descriptions set forthherein.

In one or more example embodiments, a data processing system mayestimate the grid input line-to-line voltage information directly fromthe AFE inverter terminals during an inverter self-sensing mode byestimating the inverter terminal voltage (e.g., voltage drops across theinverter switches and diodes) based on inverter gate drive signals, andsubsequently estimating the angle of the composite voltage vector, whichis constructed from the three-phase inverter terminal voltages, usingthe PLL based position detection method.

To precisely control the AFE system power factor at a grid input voltageterminal, the data processing system may compensate for a voltage dropacross the impedance between the grid input voltage terminal and the AFEinverter terminals by converting the estimated inverter voltage vectorangle from the inverter terminal voltages to the grid voltage vectorangle corresponding to the voltage at the grid input terminals.

FIG. 1 is a block diagram of a system for controlling a load accordingto some example embodiments, and FIG. 2 illustrates a method ofcontrolling the system according to some example embodiments.

Referring to FIGS. 1 and 2, a system 1000 may include a data processingsystem 100, such as a controller, an alternating current (AC)transformer 200 and an inductor resistor (LR) line filter 300 connectedto an alternating current (AC) power grid 400, an active front end (AFE)inverter 500, and an. AFE load 800. In some example embodiments, the AFEload 800 may include an inverter 600, and a load 700, such as aninterior permanent magnet (IPM) motor.

The data processing system 100 may be, but not limited to, a processor,Central Processing Unit (CPU), a controller, an arithmetic logic unit(ALU), a digital signal processor, a microcomputer, a field programmablegate array (FPGA), an Application Specific Integrated Circuit (ASIC), aSystem-on-Chip (SoC), a programmable logic unit, a microprocessor, orany other device capable of performing operations in a defined manner.In an example embodiment, the data processing system 100 may include aprocessor and a memory to support storing, processing and execution ofsoftware instructions of one or more software modules.

As discussed below, the data processing system 100 may control the AFEinverter 500 based on signals received from the AFE inverter 500.

In some example embodiments, the processor of the data processing system100 may generate Pulse Width Modulation (PWM) signals to control powerswitches of an Active Front End (AFE) inverter based on at least asynthesized grid voltage vector angle at a terminal of an alternatingcurrent (AC) grid without using physical voltage sensors at the terminalof the AC grid, and control the AFE inverter to supply power to a loadbased on the PWM signals.

In some example embodiments, the processor may generate the PWM signalsby, estimating the synthesized grid voltage vector angle at the terminalof the AC grid without using the physical voltage sensors.

In some example embodiments, the processor is configured to generate thePWM signals by, converting measured current from a measured. 3-phasecurrent in a stationary reference frame to a measured direct-quadrature(dq)-axis current in a dq rotating reference frame, generating a q-axiscurrent reference based on a AC grid terminal reference power factor,generating a d-axis current reference based on an actual DC bus voltageand a reference DC bus voltage, the actual DC bus voltage beingconnected to a load, the d-axis current reference and the q-axis currentreference forming a dq-axis current reference, generating dq-axisreference voltages based on the measured dq-axis current in the dqrotating reference frame and the dq-axis current reference, andgenerating 3-phase gate driving signals for the AFE inverter byconverting the dq-axis reference voltages based on the synthesized gridvoltage vector angle, the 3-phase gate driving signals being the PWMsignals.

In some example embodiments, the processor is configured to generate thePWM signals such that the AFE inverter maintains an actual DC busvoltage connected to the :load.

In some example embodiments, the processor is configured to estimate thesynthesized grid voltage vector angle by, estimating a terminal voltageof the AFE inverter when the inverter is enabled, the terminal voltageof the AFE inverter being a voltage of a terminal of the AFE inverter,estimating a first AFE inverter terminal voltage vector angle when theAFE inverter is disabled, the first AFE inverter terminal voltage vectorangle being an angle associated with a voltage vector of the terminal ofthe AFE inverter at an initial time, determining a second AFE inverterterminal voltage vector angle when the AFE inverter is enabled, thesecond AFE inverter terminal voltage vector angle being an angleassociated with a voltage vector of the terminal of the AFE inverter ata second time subsequent to the initial time, and estimating thesynthesized grid voltage vector angle based on the second AFE inverterterminal voltage vector angle, the synthesized grid voltage vector anglebeing an angle associated with a voltage vector of the terminal of theAC grid.

In some example embodiments, if the inverter is enabled, the processoris configured to estimate the terminal voltage of the AFE inverter by,estimating 3-phase line-to-neutral voltages of the terminal of the AFEinverter based on status signals associated with power switches of theAFE inverter and corresponding voltage drops across the power switches.

In some example embodiments, the processor is configured to estimate the3-phase line-to-neutral voltages by, examining collector-emittervoltages associated with each of the power switches of the AFE inverter.

In some example embodiments, if the inverter is disabled, the processoris configured to estimate the first AFE inverter terminal voltage vectorangle by, detecting zero-crossing instants when the voltage of theterminal of the AFE inverter crosses zero, calculating a AFE inverterterminal voltage vector angular frequency based on the zero-crossinginstants, the AFE inverter terminal voltage vector angular frequencybeing an angular frequency in rad/sec of the voltage of the terminal ofthe AFE inverter, and calculating the first AFE inverter terminalvoltage vector angle based on the AFE inverter terminal voltage vectorangular frequency and a position of an AFE inverter terminal voltagevector corresponding to a most recent one of the zero-crossing instants.

In some example embodiments, the processor is configured to estimate thesecond AFE inverter terminal voltage vector angle by, initializing aphase locking loop (PLL) using the first AFE inverter terminal voltagevector angle when the inverter is disabled, and running the phaselocking loop (PLL) using 3-phase line-to-neutral voltages of theterminal of the AFE inverter when the inverter is enabled.

In some example embodiments, the processor is configured to estimate thesecond AFE inverter terminal voltage vector angle by running the PLL toalign the second AFE inverter terminal voltage vector angle with ad-axis of a dq rotating reference frame.

In some example embodiments, when the AFE inverter is enabled, theprocessor is configured to estimate the second AFT; inverter terminalvoltage vector angle by running the PLL to continually, calculate aposition error between the second AFE inverter terminal voltage vectorangle and the d-axis, calculate an angular frequency of the second AFEinverter terminal voltage vector angle by using a PI controller toregulate the position error, and calculate the second AFE inverterterminal voltage vector angle by integrating the angular frequency.

In some example embodiments, the processor is configured to estimate theAC grid voltage vector angle by compensating for a phase shift due to avoltage drop across a filter between the terminal of the AFE inverterand the terminal of the AC grid.

In some example embodiments, the filter is one of a LCL line filter anda LR line filter.

In some example embodiments, the processor is configured to convert themeasured current from the measured 3-phase current to the measureddq-axis current based on the synthesized grid voltage vector angle.

In some example embodiments, the processor is configured to generate thed-axis current reference by, comparing the actual dc bus voltage and thereference DC bus voltage, and generating the d-axis current referenceusing a PI controller.

In some example embodiments, the processor is configured to generate theq-axis current reference based on the AC grid terminal reference powerfactor and the d-axis current reference.

In some example embodiments, the processor is configured to generate thedq-axis reference voltages by, generating a comparison signal based on aresult of comparing the d-axis current reference and the q-axis currentreference with a d-axis value of the measured dq-axis current and aq-axis value of the measured dq-axis current, respectively, andgenerating dq-axis reference voltages based on the comparison signal.

In some example embodiments, the processor is configured to, refine thesynthesized grid voltage vector angle by compensating for a time delayassociated with digital processing to generate a refined synthesizedgrid voltage vector angle; and generate the 3-phase gate driving signalsfor the AFE inverter based on the dq-axis reference voltages and therefined synthesized grid voltage vector angle, wherein the 3-phase gatedriving signals are transmitted to the AFE inverter to switch aplurality of half bridges included in the power switches of the AFEinverter.

The data processing system 100 may include a voltage sensorless positiondetecting module 110, an abc/dq Transformation Module 120, a PIcontroller 130, a reactive power control module 140, a currentregulation controller 150, and a PWM generation module 160. The voltagesensorless position detecting module 110 is shown in greater detail inFIG. 4.

As discussed below, the data processing system 100 may estimate a gridvoltage vector angle θ_(g) without using physical voltage sensorsattached to terminals of the AC grid 400, generate Pulse WidthModulation (PWM) signals to control power switches of the AFE inverter500 based on the estimated grid voltage vector angle θ_(g), and operatethe load 800 based on the PWM signals.

Referring to FIG. 2, in operation S100, the AC grid 400 may supply orconsume AC power to maintain a stable DC bus voltage V_(dc) at a DC bus.The DC bus electrically connects the AFE inverter 500 and the loadinverter 600. The DC bus may be modeled as a capacitor that consumes theelectrical power from the AC grid 400 and supplies the electrical powerto the load 800. For example, the AC grid 400 may supply power to theAFE inverter 500 when the DC bus voltage V_(dc) is less than thereference DC bus voltage V_(dc) due to the load 700 drawing more powerfrom the DC bus than the AFE inverter 500 can supply. The AC grid 400also may consume the AC power when the DC bus voltage V_(dc) is greaterthan the reference DC bus voltage V_(dc) due to the load 700, which isrunning as a generator, supplying more power to the DC bus.

In operation S200, the three-phase AC transformer 200 may convertbetween high and low three-phase AC voltage.

In operation S300, the LR line filter 300 may filter out the current:harmonics on lines. For example, the LR line filter 300 may be apre-designed LR filter. The LR line filter 300 may be embodied as longcables connected between the AFE inverter 500 and the three-phase ACtransformer 200, the length of which is determined based on the currentharmonics on the lines.

In other example embodiments, the system 1000 may include ainductor-capacitor-inductor style filter or LCL filter (not shown)between the AFE inverter 500 and the three-phase AC transformer 200rather than the LR filter 300, such that the data processing system 100is configured to compensate for a phase shift due to a voltage dropacross the LCL filter (not shown).

In operation S400, the data processing system 100 may estimate the gridvoltage vector angle θ_(g), generate the Pulse Width Modulation (PWM)signals to control power switches of the AFE inverter 500 based on theestimated grid voltage vector angle θ_(g). Operation S400 is discussedin greater detail below with reference to the sub-operations illustratedin FIG. 4.

For example, the voltage sensorless position detecting module 110 mayestimate the grid voltage vector angle θ_(g) defined as the d-axisorientation of the rotating dq-axis frame without using physical voltagesensors attached to the AC grid terminals 400. Thereafter, the dataprocessing system 100 may generate the Pulse Width Modulation (PWM)signals to control the power switches of the AFE inverter 500 based onthe estimated grid voltage vector angle θ_(g).

Details on the operation of the data processing system 100 including theestimation of the grid voltage vector angle θ_(g) by the voltagesensorless position detecting module 110, and the generation of the PWMsignals based thereon will be discussed below with reference to FIGS. 3to 11.

In operation S500, the AFE inverter 500 may supply/consume power to/fromthe AC grid 400 to regulate the DC bus voltage. For example, the AFEinverter 500 may consume power from the AC grid 400 when the DC busvoltage is less than the reference DC bus voltage V*_(dc).Alternatively, the AFE inverter 500 may supply power back to the AC grid400 when the DC bus voltage is greater than the reference DC bus voltageV*_(dc).

The AFE inverter 500 may include power electronics, such as switchingsemiconductors to generate, modify and/or control the PWM signals orother alternating current signals (e.g., pulse, square wave, sinusoidal,or other waveforms) applied to the DC bus to operate the load 800.

In operation S600, the inverter 600 may supply/consume electric powerto/from the load 700. For example, the inverter 600 may supply theelectric power to the load 700. In this case, the inverter 600 drawspower from the DC bus. Alternatively, the inverter 600 may also consumemechanical power from the load 700, when the load 700 is running as agenerator. In this case, the inverter 600 supplies electric power to theDC bus.

The inverter 600 may include power electronics, such as switchingsemiconductors to generate, modify and control pulse-width modulatedsignals or other alternating current signals (e.g., pulse, square wave,sinusoidal, or other waveforms) applied to the load 700. A separate PWMgeneration module provides inputs to a driver stage within the inverter600. An output stage of the inverter 600 provides the pulse-widthmodulated voltage waveform or other voltage signal to control the load700. In an example embodiment, the inverter 600 is powered by the directcurrent (dc) voltage bus voltage V_(dc).

In operation S700, the load 700 may consume power from the inverter 600.In this case, the inverter 600 consumes power from the DC bus.Alternatively, the load 700 may also supply power to the inverter 600and the inverter 600 may supply the power back to the DC bus, when theload 700 runs as a generator.

FIG. 3 illustrates a method of operating a controller to perform avoltage sensorless position detecting in a system according to someexample embodiments.

Referring to FIGS. 1 to 3, in operation S400 illustrated in FIG. 2, thedata processing system 100 may estimate the grid voltage vector angleθ_(g), and generate the Pulse Width Modulation (PWM) signals to controlthe power switches of the AFE inverter 500 based on the estimated gridvoltage vector angle θ_(g) by performing operations S110 to S160,discussed below.

In operation S110, the voltage sensorless position detecting module 110may receive the power switch status information from the AFE inverter500 when inverter switching is enabled, receive the detected phasevoltage zero-crossing signals from the AFE inverter 500 when theinverter switching is disabled, and estimate the grid voltage vectorangle θ_(g) defined as the d-axis orientation of the rotating dq-axisbased thereon without using physical voltage sensors attached to the ACgrid terminals 400. Therefore, the bulky and costly external voltagesensors can be removed from the AFE control system. Operation S110 willbe discussed in more detail below with reference to FIGS. 4 to 11.

In operation S120, the abc/dq Transformation Module 120 may receive the3-phase grid currents I_(c), I_(b), I_(a) and perform the Clarke/Parktransformation (abc-to-dq) based on the estimated grid voltage vectorangle θ_(g) to convert the 3-phase grid currents into the q-axis currentI_(q) and the d-axis current I_(d) in the dq rotating reference frame.

The dq axis current may refer to the direct axis current and thequadrature axis current in the dq rotating reference frame as applicablein the context of vector-controlled alternating current machines, suchas the load 700.

The abc/dq Transformation Module 120 may apply a Clarke transformationand a Park transformation or other conversion equations (e.g., certainconversion equations that are suitable and are known to those ofordinary skill in the art) to convert the measured three-phaserepresentations of current: into two-phase representations of currentbased on the current data I_(a), I_(b), and I_(c) and the estimated gridvoltage vector angle θ_(g).

In operation S130, the PI controller 130 may receive a differencebetween the measured DC bus voltage V_(dc) and a reference DC busvoltage V*_(dc), and may generate the d-axis reference current I*_(d)based on the difference between the detected DC bus voltage V_(dc) andthe reference DC bus voltage V*_(dc). The PI controller is a closed loopproportional-integral controller used for the measured DC bus voltageV_(dc) to track the reference DC bus voltage V*_(dc).

In operation S140, the reactive power control module 140 may generatethe q-axis reference current I*_(q) based on a reference power factorPF* received from a high-level system control unit (not shown). Thereference power factor PF* may be empirically determined for the system1000 based on users' system control requirements. The q-axis referencecurrent I*_(q) is generated to assure the system 1000 is satisfying therequirement on the reference power factor PF* with the determined d-axisreference current I*_(d) from the operation S140.

In operation S150, the current regulation controller 150 may utilize thed-axis reference current I*_(d) and the q-axis reference current I*_(q)as reference currents to generate the dq axis reference voltage V*_(d)and V*_(q). For example, the current regulation controller 150 mayreceive the difference between I_(q) and I*_(q), and the differencebetween I_(d) and I*_(d), and may generate dq axis reference voltageV*_(d) and V*_(q) therefrom. The current: regulation controller 150 mayinclude two closed loop PI controllers along with a dq-axiscross-coupling decoupling module to track the d-axis current I_(d) andthe q-axis current I_(q) to their respective references I_(d)* andI_(q)*. The outputs from the d-axis current regulator and q-axis currentregulator are the d-axis reference voltage V*_(d) and q-axis referencevoltage V*_(q).

In operation S160, the PWM generation module 160, may receive the dqaxis reference voltage V*_(d) and V*_(q) in the dq rotating referenceframe from the current regulation controller 150, and convert dq axisreference voltage V*_(d) and V*_(q) in the dq rotating reference frameto an α-axis voltage command v*_(α) and a β-axis voltage command v*_(β)in the α-β stationary frame based on the estimated grid voltage vectorangle θ_(g), and then convert the α-axis voltage command v*_(α) andβ-axis voltage command v*_(β) from two phase data representations intothree-phase data representations (e.g., three-phase representations,such as PWM duty A, duty B and duty C for three phases). The PWMgeneration module 160 may generate the three phase power switch gatesignals for the gate drive control of the inverter power switches of theAFE inverter 500 based on the three-phase PWM duty representations.

In other example embodiments, the PWM generation module 160 may furtherprocess the estimated grid voltage vector angle θ_(g) to generate arefined estimated grid voltage vector angle θ_(g)′ by extrapolating theestimated grid voltage vector angle θ_(g) by one and half controlperiods using the PLL generated frequency to compensate for a delayassociated with the digital processing. Thereafter, the PWM generationmodule 160 may use the refined estimated grid voltage vector angleθ_(g)′ to convert the dq axis reference voltage V*_(d) and V*_(q) to theα-β voltage commands v*_(α) and v*_(β) in the α-β reference frame.

FIG. 4 illustrates a voltage sensorless position detecting moduleaccording to some example embodiments, and FIG. 5 illustrates a methodof operating a voltage sensorless position detecting module according tosome example embodiments.

Referring to FIGS. 4 and 5, the voltage sensorless position detectingmodule 110 may include an inverter terminal voltage estimating module112, an inverter terminal voltage vector angle detecting module 114, agrid voltage vector angle estimating module 116, and an initial gridvoltage vector angle detecting module 118.

In operation S110 illustrated in FIG. 3, the voltage sensorless positiondetecting module 110 of the data processing system 100 may estimate thegrid voltage vector angle θ_(g), by performing operations S112 to S118illustrated in FIG. 5, discussed below.

In operation S112, the inverter terminal voltage estimating module 112may estimate the inverter terminal voltages Van, Vbn and Vcn based onthe power switch status information (or, alternatively, ON/OFF statussignals) and a diode voltage drop across the power switches from the AFEinverter 500. Operation S112 will be discussed below in more detail withreference to FIG. 6.

In operation S114, the inverter terminal voltage vector angle detectingmodule 114 may generate the inverter terminal voltage vector angle θ_(i)based on the inverter terminal voltages Van, Vbn and Vcn received fromthe inverter terminal voltage estimating module 112 and the initialinverter voltage vector angle θ_(i) _(_) _(init). The inverter terminalvoltage vector angle detecting module 114 may include a Proportional andIntegration (PI) controller (see FIG. 7) to regulate the position errorto force the q-axis voltage V_(q) in the dq rotating reference frame to0 such that the output of the PI controller will be the inverterterminal voltage vector angular frequency ω. Operation S114 will bediscussed below in more detail with reference to FIGS. 7 and 8.

In operation S116, the grid voltage vector angle estimating module 116may estimate the grid voltage vector angle θ_(g) without using physicalvoltage sensors based on the inverter terminal voltage vector angleθ_(i) received from the inverter terminal voltage vector angle detectingmodule 114. Operation S116 will be discussed below in more detail withreference to FIG. 9.

As discussed above, the grid voltage vector angle estimating module 116may provide the estimated grid voltage vector angle θ_(g) to the abc/dqTransformation Module 120, and the abc/dq Transformation Module 120 mayuse the estimated grid voltage vector angle θ_(g) to perform abc-to-dqtransformation on the 3-phase grid currents I_(a), I_(b) and I_(c) toconvert the 3-phase grid currents I_(a), I_(b) and I_(c) into the q-axiscurrent I_(q) and the d-axis current I_(d) in the dq rotating referenceframe.

In operation S118, the initial grid voltage vector angle detectingmodule 118 may receive phase voltage zero-crossing signals from the AFEinverter 500, and may generate an initial inverter voltage vector angleθ_(i) _(_) _(init) to initialize the Phase Locked Loop (PLL) controllerin the inverter terminal voltage phase angle detecting module 114.Therefore, the PLL controller may start with the correct initialinverter terminal voltage vector angle θ_(i) _(_) _(init). In theinverter terminal voltage vector angle detecting module 114, the PLLcontroller is utilized to detect the inverter terminal voltage vectorangle θ_(i). Operation S118 will be discussed below in more detail withreference to FIG. 10.

FIG. 6 illustrates a method of estimating the inverter terminal voltageaccording to some example embodiments, and FIG. 12 is a circuit diagramillustrating an AFE inverter connected to a load according to someexample embodiments.

Referring to FIGS. 1 to 6 and 12, in operation S112-1, the invertertermination voltage estimating module 112 may determine the phasecurrent direction based on the power switch status information. For anexample, the direction of the phase A current is defined as positivedirection (+la) when the phase A top switch (see FIG. 12) is ON.

In operation S112-2, the inverter termination voltage estimating module112 may calculate the instantaneous phase voltage V_(aN) V_(bN) andV_(cN) using the following equations.

If the phase current I_(x) (subscript ‘X’ represents phase a, b or c) ispositive (the case illustrated in FIG. 12), the following instantaneousV_(XN) (subscript ‘X’ represents phase a, b or c) values can becalculated:

V _(XN)=(Vdc−V _(igbt))=Top switch ON

OR

V _(XN)=(−V _(diode))=Top switch OFF   Eq. 1

If phase current I_(x) is negative, the following instantaneous V_(XN)values can be calculated:

V _(XN)=(Vdc+V _(igbt))=Bottom switch OFF

OR

V _(XN)=(+V _(diode))=Bottom switch ON   Eq. 2

In operation S112-3, the inverter termination voltage estimating module112 may calculate the line-to-line voltage V_(ab) between terminal a andterminal b of the AFE inverter 500 and V_(ca) between terminal c andterminal a of the AFE inverter 500 using the following equations:

V _(ab) =V _(aN) −V _(bN)

V _(ca) =V _(cN) −V _(aN)   Eq. 3

The voltage V_(xN) (subscript ‘X’ represents phase a, b or c) inequation 3 between the AFE inverter terminal X and a negative rail ofthe DC bus is estimated by examining the inverter power switch collectorto emitter voltages.

However, the line-to-line voltages V_(ab) and V_(ca) are just oneexample of line-to-line voltages, and the inverter termination voltageestimating module 112 may calculate other line-to-line voltages betweenvarious terminals of the AFE inverter 500.

In operation S112-4, the inverter termination voltage estimating module112 may calculate the line-to-neutral voltage Van, Vbn and Vcn using thefollowing equations:

V _(an)=1/3(V _(ab) −V _(ca))

V _(bn)=−1/3(2V _(ab) +V _(ca))

V _(cn)=1/3(V _(ab)+2V _(ca))   Eq. 4

Therefore, the inverter voltage vector angle θ_(i) can be estimated inoperation S114 using the line-to-neutral voltage V_(an) V_(bn) andV_(cn). Therefore, in one or more example embodiments, the system 1000can detect the inverter terminal voltages V_(an) V_(bn) and V_(cn)without using physical voltage sensors at the terminals of the AC grid400.

FIG. 7 illustrates a block diagram of an inverter terminal voltagevector angle detecting module 114 and FIG. 8 illustrates a method ofestimating the inverter terminal voltage vector angle according to someexample embodiments.

Referring to FIGS. 1 to 5, 7 and 8, in operation S114-1, the inverterterminal voltage vector angle detecting module 114 may calculate thed-axis voltage V_(d) and the q-axis voltage V_(q) in the rotating dqreference frame based on the inverter terminal line-to-neutral voltageV_(an), V_(bn), V_(cn) and the inverter terminal voltage vector angleθ_(i) using the Park transformation in the following equation:

$\begin{matrix}{{V_{\alpha} = {{\frac{2}{3}V_{an}} - {\frac{1}{3}( {V_{bn} - V_{cn}} )}}}{V_{\beta} = {\frac{2}{\sqrt{3}}( {V_{bn} - V_{cn}} )}}{V_{d} = {{V_{\alpha} \cdot {\cos ( \theta_{i} )}} + {V_{\beta} \cdot {\sin ( \theta_{i} )}}}}{V_{q} = {{V_{\beta} \cdot {\cos ( \theta_{i} )}} - {V_{\alpha} \cdot {\sin ( \theta_{i} )}}}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

In operation S114-2, the inverter terminal voltage vector angledetecting module 114 may calculate a position error Δθ_(i). The inverterterminal voltage vector angle detecting module 114 may calculate theposition error Δθ_(i) using the following Equation:

$\begin{matrix}{{\Delta\theta}_{i} = {{a\tan}( \frac{V_{q}}{V_{d}} )}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

In operation S114-3, the inverter terminal voltage vector angledetecting module 114 calculate the phase angular frequency ω based onthe position error Δθ_(i).

For example, the inverter terminal voltage vector angle detecting module114 may use a PI controller to regulate the position error Δθ_(i) toforce the q-axis voltage V_(q) to 0, which means the d-axis in therotating dq reference frame will be forced to align to the grid voltagevector, so the output of the PI controller is the grid voltage vectorangular frequency ω.

In operation S114-4, the inverter terminal voltage vector angledetecting module 114 may utilize the following equation to calculate theangle θ_(i) of the inverter voltage vector u_(s):

θ_(i)=∫₀ ^(t) ω·dt+θ _(i) _(_) _(init)   Eq. 7

Thereafter, the inverter terminal voltage vector angle detecting module114 may return to operation S114-1, and recalculate the d-axis voltageV_(d) and the q-axis voltage V_(q) such that operations S114-1 to S114-4are performed iteratively in a phase locked loop (PLL) to reach aconvergence.

Operations S114-1 to S114-4 are illustrated in FIG. 7 in block diagramform.

FIG. 9 illustrates a method of estimating the grid voltage vector angleθ_(g) according to some example embodiments. FIGS. 11A to 11C are vectordiagrams illustrating current and voltage vectors in the dq rotatingreference frame according to some example embodiments.

Referring to FIGS. 11A to 11C, in FIGS. 11A to 11C, Δv is a voltagevector difference between an inverter terminal voltage vector u_(s) at aterminal of the AFE inverter 500, and the grid voltage vector u_(g) at aterminal of the AC grid 400, i.e., Δv=u_(s)−u_(g). The angle β is anangle between a q-axis voltage vector V_(q) and the voltage vectordifference Δv, the angle α is an angle between a d-axis voltage vectorV_(d) and a vector jωLi_(s). In FIGS. 11A to 11C, the angles α and β areused as intermediate calculation angles to calculate an adjusted angle θrepresenting the difference between θ_(i) and θ_(g), and the angle ψ isa power factor angle. The angles Ψ, β and α are defined as below:

$\begin{matrix}{{\psi = {\cos^{- 1}( {{PF}^{*}} )}}{\alpha = {\frac{\pi}{2} - \psi}}{0<=\beta<=\frac{\pi}{2}}} & {{Eq}.\mspace{14mu} 8}\end{matrix}$

Since 0<=|PF*|<=1,

$\begin{matrix}{0 = {< \psi<=\frac{\pi}{2}}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$

In FIG. 11A, since the absolute value of the reference power factor PF*is 1, the AFE inverter 500 supplies/consumes power to/from the AC grid400 at a unity reference power factor PF*. In graph A1, the AFE inverter500 supplies power to the AC grid 400. In graph A2, the AFE inverter 500consumes power from the AC grid 400. In both cases, the power factorangle ψ equals 0 (Is>0 and Is<0) and the angle α is:

$\begin{matrix}{\alpha = {{\frac{\pi}{2} - \psi} = {{\frac{\pi}{2} - 0} = \frac{\pi}{2}}}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

In the following equations, R and L are the resistance and inductancevalues of the LR line filter 300, respectively; I_(s) is the signedmagnitude of an AFE inverter phase current reference vector i_(s).

$\begin{matrix}{I_{s} = \{ \begin{matrix}{{{{sign}( I_{d}^{*} )} \cdot \sqrt{( I_{d}^{*} )^{2} + ( I_{q}^{*} )^{2}}},} & {{{when}\mspace{14mu} I_{d}^{*}} \neq 0} \\{{{- {{sign}( I_{q}^{*} )}} \cdot \sqrt{( I_{d}^{*} )^{2} + ( I_{q}^{*} )^{2}}},} & {{{when}\mspace{14mu} I_{d}^{*}} = 0}\end{matrix} } & {{Eq}.\mspace{14mu} 11}\end{matrix}$

where I*_(d) is the d-axis current reference generated from the PIcontroller 130 and I*_(q) is the q-axis current reference generated fromthe reactive power control module 140.

From graph A1, when (I_(s)>0 & |PF*|=1), β, V_(d) and V_(q) can becalculated using the following equations:

β=tan⁻¹(R/ωL)

V _(d) =u _(g) +I _(s) ·R=u _(g) +Δv·sin(β)=u _(g)+sin(β)·I_(s)·√{square root over (R ²+(ω·L)²)}

V _(q) =ω·L·I _(s) =Δv·cos(β)=cos(β)·I _(s)·√{square root over (R²+(ω·L)²)}  Eq. 12

From graph A2, when (I_(s)<0 & |PF*|=1), β, V_(d) and V_(q) can becalculated using the following equations:

$\begin{matrix}{{\beta = {\tan^{- 1}( {R/{\omega L}} )}}\begin{matrix}{V_{d} = {{u_{g} + {{I_{s}} \cdot R}} = {{u_{g} - {{\Delta v} \cdot {\sin (\beta)}}} = {u_{g} - {{\sin (\beta)} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}}}} \\{= {u_{g} + {{\sin (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{V_{q} = {{{- \omega} \cdot L \cdot {I_{s}}} = {{{- {\Delta v}} \cdot {\cos (\beta)}} = {{- {\cos (\beta)}} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}}} \\{= {{\cos (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}\end{matrix}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

In FIG. 11B, the AFE inverter 500 supplies power to the AC grid 400 at anon-unity reference power factor PF*. In graph B1, the reference powerfactor PF* is greater than 0, and the inverter current vector i_(s)leads the grid voltage vector u_(g). In graph B2, the reference powerfactor PF* is less than 0, and the grid voltage vector u_(g) leads theinverter current vector i_(s).

From graph B1, when (I_(s)>0 & PF*>0), β, V_(d) and V_(q) can becalculated using the following equations:

β=(π/2−α)−tan⁻¹(R/ωL)=ψ−tan⁻¹(R/ωL)

V _(d) =u _(g) −Δv·sin(β)=u _(g)−sin(β)·I _(s)·√{square root over (R²+(ω·L)²)}

V _(q) =Δv·cos(β)=cos(β)·I _(s)·√{square root over (R ²+(ω·L)²)}  Eq. 14

From graph B2, when (I_(s)>0 & PF*<0), β, V_(d) and V_(q) can becalculated using the following equations:

β=(π/2−α)+tan⁻¹(R/ωL)=ψ+tan⁻¹(R/ωL)

V _(d) =u _(g) +Δv·sin(β)=u _(g)+sin(β)·I _(s)·√{square root over (R²+(ω·L)²)}

V _(q) =Δv·cos(β)=cos(β)·I _(s)·√{square root over (R ²+(ω·L)²)}  Eq. 15

In FIG. 11C, the AFE inverter 500 consumes power from the AC grid 400 ata non-unity reference power factor PF*. In graph C1, the reference powerfactor PF* is greater than 0, and the reversed inverter current vectori_(s) leads the grid voltage vector u_(g). In graph C2, the referencepower factor PF* is less than 0, and the grid voltage vector u_(g) leadsthe reversed inverter current vector i_(s).

From graph C1, when (I_(s)<0 & PF*>0), V_(d) and V_(q) can be calculatedusing the following equations:

$\begin{matrix}{{\beta = {{( {{\pi/2} - \alpha} ) - {\tan^{- 1}( {R/{\omega L}} )}} = {\psi - {\tan^{- 1}( {R/{\omega L}} )}}}}\begin{matrix}{V_{d} = {u_{g} + {{\Delta v} \cdot {\sin (\beta)} \cdot u_{g}} + {{\sin (\beta)} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{= {u_{g} - {{\sin (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{V_{q} = {{{- {\Delta v}} \cdot {\cos (\beta)}} = {{- {\cos (\beta)}} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{= {{\cos (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}\end{matrix}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

From graph C2, when (I_(s)<0 & PF*<0), V_(d) and V_(q) can be calculatedusing the following equations:

$\begin{matrix}{{\beta = {{( {{\pi/2} - \alpha} ) + {\tan^{- 1}( {R/{\omega L}} )}} = {\psi + {\tan^{- 1}( {R/{\omega L}} )}}}}\begin{matrix}{V_{d} = {u_{g} - {{\Delta v} \cdot {\sin (\beta)} \cdot u_{g}} - {{\sin (\beta)} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{= {u_{g} + {{\sin (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{V_{q} = {{{- {\Delta v}} \cdot {\cos (\beta)}} = {{- {\cos (\beta)}} \cdot {I_{s}} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}} \\{= {{\cos (\beta)} \cdot I_{s} \cdot \sqrt{R^{2} + ( {\omega \cdot L} )^{2}}}}\end{matrix}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

As discussed in more detail below with reference to FIG. 9, based onanalysis above for all cases in FIGS. 11A to 11C, the grid voltagevector angle estimating module 116 may select different ones of thefollowing equations to calculate the adjusted angle θ from the AFEinverter 500 terminal to the AC grid 400 terminal:

$\begin{matrix}\begin{matrix}{\psi = {\cos^{- 1}( {{PF}^{*}} )}} \\\{ \begin{matrix}{{\beta = {\psi - {\tan^{- 1}( {R/{\omega L}} )}}},{{{when}\mspace{14mu} 1} > {PF}^{*}>=0}} \\{{\beta = {\psi + {\tan^{- 1}( {R/{\omega L}} )}}},{{{when}\mspace{14mu} {{PF}^{*}}} = {{1\mspace{14mu} {or}\mspace{14mu} {PF}^{*}} < 0}}}\end{matrix}  \\\{ \begin{matrix}\begin{matrix}{{V_{d} = {u_{g} - {{\sin (\beta)} \times I_{S} \times \sqrt{R^{2} + ( {\omega L} )^{2}}}}},} \\{{{when}\mspace{14mu} 1} > {PF}^{*}>=0}\end{matrix} \\\begin{matrix}{{V_{d} = {u_{g} + {{\sin (\beta)} \times I_{S} \times \sqrt{R^{2} + ( {\omega L} )^{2}}}}},} \\{{{when}\mspace{14mu} {{PF}^{*}}} = {{1\mspace{14mu} {or}\mspace{14mu} {PF}^{*}} < 0}}\end{matrix}\end{matrix}  \\{V_{q} = {{\cos (\beta)} \times {I_{S}} \times \sqrt{R^{2} + ( {\omega L} )^{2}}}} \\\{ \begin{matrix}{{\theta = {- {\tan^{- 1}( \frac{V_{q}}{V_{d}} )}}},{{{when}\mspace{14mu} I_{S}}>=0}} \\{{\theta = {\tan^{- 1}( \frac{V_{q}}{V_{d}} )}},{{{when}\mspace{14mu} I_{S}} < 0}}\end{matrix} \end{matrix} & {{Eq}.\mspace{14mu} 18}\end{matrix}$

Therefore, the compensated position considering phase shift between theinverter terminal voltage vector angle θ_(i) and the grid voltage vectorangle θ_(g) can be calculated using the following equation:

θ_(g)=θ_(i)+θ  Eq. 19

Referring to FIGS. 1 to 5, 9 and 11A to 11C, using various ones ofEquations 18 and 19, discussed above, the grid voltage vector angleestimating module 116 may calculate the grid voltage vector angle θ_(g).

In operation S116-1, the grid voltage vector angle estimating module 116may calculate the requested power factor angle Ψ based on the referencepower factor PF* using the following Equation:

Ψ=cos⁻¹(|PF*|).   Eq. 20

In operation S116-2, the grid voltage vector angle estimating module 116may determine whether the absolute value of the reference power factorPF* is equal to 1 or whether the reference power factor PF* is less thanzero, and the grid voltage vector angle estimating module 116 will usethis information about the reference power factor PF* to determine whichof the equations included in Equation 18 will be used to calculate theintermediate calculation angle β and the d-axis voltage V_(d).

In operation S116-3, the grid voltage vector angle estimating module 116may calculate the intermediate calculation angle β based on the powerfactor angle Ψ determined in operation S116-1, the grid voltage vectorangular frequency ω calculated in operation S114, and known line filterparameters L and R, which are the inductance and resistance values ofthe LR line filter 300, respectively. Further, the grid voltage vectorangle estimating module 116 may calculate the d-axis voltage V_(d) basedon the intermediate calculation angle β, the line filter parameters Rand L, the grid voltage vector angular frequency ω calculated inoperation S114, the signed magnitude of the AFE inverter phase currentvector reference i_(s), and a magnitude of the d voltage vector u_(g).

The grid voltage vector angle estimating module 116 may calculate theangle β and d-axis voltage V_(d) using different ones of the equationsincluded in Equation 18 based on the reference power factor PF*.

For example, if the absolute value of the reference power factor PF* isequal to 1 or the reference power factor is less than zero, the gridvoltage vector angle estimating module 116 may determine the angle β andV_(d) using the following equations:

β=ψ+tan⁻(R/ωL)

V _(d) =u _(g)+sin(β)×I _(s)×√{square root over (R ²+(ωL)²)}  Eq. 20

Alternatively, if the absolute value of the reference power factor PF*is not equal to 1 or the reference power factor PF* is greater than orequal to zero, the grid voltage vector angle estimating module 116 maydetermine the angle β and V_(d) using the following two equations:

β=ψ−tan⁻¹(R/ωL)

V _(d) =u _(g)−sin(β)×I _(s)×√{square root over (R ²+(ωL)²)}  Eq. 21

In operation S116-4, the grid voltage vector angle estimating module 116may calculate the q-axis voltage V_(q) based on the angle β determinedin operation S116-3, the line filter parameters L and R, the gridvoltage vector angular frequency ca calculated in operation S114, andthe magnitude of the AFE inverter phase current vector reference I_(s).For example, the grid voltage vector angle estimating module maycalculate V_(q) using the following Equation:

V _(q)=cos(β)×|I _(s)|×√{square root over (R ²+(ωL)²)}  Eq. 22

In operation S116-5, the grid voltage vector angle estimating module 116may determine whether the signed magnitude of the inverter phase currentvector I_(s) is positive or negative, and the grid voltage vector angleestimating module 116 may determine which of the equations in Equation18 to use to calculate the adjusted angle θ based on the signedmagnitude of the inverter phase current vector I_(s).

In operation S116-6, the grid voltage vector angle estimating module 116may calculate the adjusted angle θ based on the equation determined inoperation S116-5, such that different ones of the equations included in.Equation 18 are utilized to determine the adjusted angle θ based on thesigned magnitude of the inverter phase current vector I_(s)

In operation S116-7, the grid voltage vector angle estimating module 116may calculate the grid voltage vector angle θ_(g) based on the adjustedangle θ determined in operation S116-6 and the inverter terminal voltagevector angle θ_(i) determined in operation S114.

FIG. 10 illustrates a method of generating an initial inverter terminalvoltage vector angle according to some example embodiments.

Referring to FIGS. 1 to 5 and 10, in operation S118-1, the initialinverter terminal voltage vector angle detecting module 118 may detectthe inverter terminal voltage zero-crossing instants and record the timestamps when the AFE inverter 500 is disabled. For example, a hardwaredevice, such as a PSoC chip, can baa utilized to detect thezero-crossing instants of the inverter terminal voltage u_(s).

Based on the recorded time stamps information at each zero-crossinginstant, the initial inverter terminal voltage vector angle detectingmodule 118 may estimate the angle θ_(i) of the inverter terminal voltagevector u_(s) before the AFE inverter 500 is enabled, and use theestimated angle θ_(i) of the inverter terminal voltage vector u_(s) toinitialize the PLL controller.

In operation S118-2, the initial terminal voltage vector angle detectingmodule 118 may calculate the inverter terminal voltage angular frequencyω based on the inverter terminal voltage zero-crossing instants beforethe AFE inverter 500 is enabled. For example, the initial terminalvoltage vector angle detecting module 118 may calculate the inverterterminal voltage angular frequency ω in rad/sec using the followingEquation:

ω=π/Δt,   Eq. 23

where Δt is the time stamp difference in seconds between twozero-crossing instants.

In operation S118-3, the initial terminal voltage vector angle detectingmodule 118 may calculate the initial inverter terminal voltage vectorangle θ_(i) _(_) _(init) based on the inverter terminal voltage angularfrequency ω. For example, the initial inverter terminal voltage vectorangle detecting module 118 may calculate the initial inverter terminalvoltage vector angle θ_(i) _(_) _(init) using the following Equation:

θ_(i) _(_) _(init)=∫₀ ^(i) ω·dt+θ _(zero) _(_) _(crossing)   Eq. 24

where θ_(i) _(_) _(init) is the calculated initial inverter terminalvoltage vector angle and θ_(zero) _(_) _(crossing) is the inverterterminal voltage vector angle corresponding to the most recentzero-crossing instant.

The initial terminal voltage vector angle detecting module 118 mayprovide the initial inverter terminal voltage vector angle θ_(i) _(_)_(init) to the inverter terminal voltage vector angle detecting module114. As discussed above, the inverter terminal voltage vector angledetecting module 114 may use the initial inverter terminal voltagevector angle θ_(i) _(_) _(init) to initialize the integrator of the PLLcontroller in the inverter terminal voltage vector angle detectingmodule 114. Therefore, the PLL controller may start with the correctinitial inverter terminal voltage vector angle θ_(i) _(_) _(init)without using the bulkiness of sensors at the AC grid terminal 400.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of example embodiments, and allsuch modifications as would be obvious to one skilled in the art areintended to be included within the scope of the claims.

1. A controller comprising: a memory having computer-readableinstructions stored therein; and a processor configured to execute thecomputer-readable instructions to, estimate a synthesized grid voltagevector angle at a terminal of an alternating current (AC) grid withoutusing physical voltage sensors at the terminal of the AC grid by,estimating a terminal voltage of an Active Front End (AFE) inverter whenthe AFE inverter is enabled, the terminal voltage of the AFE inverterbeing a voltage of a terminal of the AFE inverter, estimating a firstAFE inverter terminal voltage vector angle when the AFE inverter isdisabled, the first AFE inverter terminal voltage vector angle being anangle associated with the voltage vector of the terminal of the AFEinverter at an initial time, determining a second AFE inverter terminalvoltage vector angle when the AFE inverter is enabled, the second AFEinverter terminal voltage vector angle being an angle associated withthe voltage vector of the terminal of the AFE inverter at a second timesubsequent to the initial time, and estimating the synthesized gridvoltage vector angle based on the second AFE inverter terminal voltagevector angle, the synthesized grid voltage vector angle being an angleassociated with a voltage vector at the terminal of the AC grid;generate Pulse Width Modulation (PWM) signals to control power switchesof the AFE inverter based on at least (i) the synthesized grid voltagevector angle at the terminal of the AC grid and (ii) a AC grid terminalreference power factor the AC grid terminal reference power factorrepresenting a desired phase shift between the voltage vector and acurrent vector at the terminal of the AC grid; and control the AFEinverter to supply power to a load based on the PWM signals. 2.(canceled)
 3. The controller of claim 1, wherein the processor isconfigured to generate the PWM signals by, converting measured currentfrom a measured 3-phase current in a stationary reference frame to ameasured direct-quadrature (dq)-axis current in a dq rotating referenceframe, generating a q-axis current reference based on the AC gridterminal reference power factor, generating a d-axis current referencebased on an actual DC bus voltage and a reference DC bus voltage, theactual DC bus voltage being connected to the load, the d-axis currentreference and the q-axis current reference forming a dq-axis currentreference, generating dq-axis reference voltages based on the measureddq-axis current in the dq rotating reference frame and the dq-axiscurrent reference, and generating 3-phase gate driving signals for theAFE inverter by converting the dq-axis reference voltages based on thesynthesized grid voltage vector angle, the 3-phase gate driving signalsbeing the PWM signals.
 4. The controller of claim 1, wherein theprocessor is configured to generate the PWM signals such that the AFEinverter maintains an actual DC bus voltage connected to the load. 5.(canceled)
 6. The controller of claim 1, wherein, if the inverter isenabled, the processor is configured to estimate the terminal voltage ofthe AFE inverter by, estimating 3-phase line-to-neutral voltages of theterminal of the AFE inverter based on status signals associated withpower switches of the AFE inverter and corresponding voltage dropsacross the power switches.
 7. The controller of claim 6, wherein theprocessor is configured to estimate the 3-phase line-to-neutral voltagesby, examining collector-emitter voltages associated with each of thepower switches of the AFE inverter.
 8. The controller of claim 1,wherein, if the inverter is disabled, the processor is configured toestimate the first AFE inverter terminal voltage vector angle by,detecting zero-crossing instants when the voltage of the terminal of theAFE inverter crosses zero, calculating a AFE inverter terminal voltagevector angular frequency based on the zero-crossing instants, the AFEinverter terminal voltage vector angular frequency being an angularfrequency in rad/sec of the voltage of the terminal of the AFE inverter,and calculating the first AFE inverter terminal voltage vector anglebased on the AFE inverter terminal voltage vector angular frequency anda position of an AFE inverter terminal voltage vector corresponding to amost recent one of the zero-crossing instants.
 9. The controller ofclaim 1, wherein the processor is configured to estimate the second AFEinverter terminal voltage vector angle by, initializing a phase lockingloop (PLL) using the first AFE inverter terminal voltage vector anglewhen the inverter is disabled, and running the phase locking loop (PLL)using 3-phase line-to-neutral voltages of the terminal of the AFEinverter when the inverter is enabled.
 10. The controller of claim 9,wherein the processor is configured to estimate the second AFE inverterterminal voltage vector angle by running the PLL to align the second AFEinverter terminal voltage vector angle with a d-axis of a dq rotatingreference frame.
 11. The controller of claim 10, wherein, when the AFEinverter is enabled, the processor is configured to estimate the secondAFE inverter terminal voltage vector angle by running the PLL tocontinually, calculate a position error between the second AFE inverterterminal voltage vector angle and the d-axis, calculate an angularfrequency of the second AFE inverter terminal voltage vector angle byusing a PI controller to regulate the position error, and calculate thesecond AFE inverter terminal voltage vector angle by integrating theangular frequency.
 12. The controller of claim 1, wherein the processoris configured to estimate the AC grid voltage vector angle bycompensating for an actual phase shift due to a voltage drop across afilter between the terminal of the AFE inverter and the terminal of theAC grid.
 13. The controller of claim 12, wherein the filter is one of aLCL line filter and a LR line filter.
 14. The controller of claim 3,wherein the processor is configured to convert the measured current fromthe measured 3-phase current to the measured dq-axis current based onthe synthesized grid voltage vector angle.
 15. The controller of claim3, wherein the processor is configured to generate the d-axis currentreference by, comparing the actual dc bus voltage and the reference DCbus voltage, and generating the d-axis current reference using a PIcontroller.
 16. The controller of claim 3, wherein the processor isconfigured to generate the q-axis current reference based on the AC gridterminal reference power factor and the d-axis current reference. 17.The controller of claim 3, wherein the processor is configured togenerate the dq-axis reference voltages by, generating a comparisonsignal based on a result of comparing the d-axis current reference andthe q-axis current reference with a d-axis value of the measured dq-axiscurrent and a q-axis value of the measured dq-axis current,respectively, and generating dq-axis reference voltages based on thecomparison signal.
 18. The controller of claim 3, wherein the processoris configured to, refine the synthesized grid voltage vector angle bycompensating for a time delay associated with digital processing togenerate a refined synthesized grid voltage vector angle, and generatethe 3-phase gate driving signals for the AFE inverter based on thedq-axis reference voltages and the refined synthesized grid voltagevector angle, wherein the 3-phase gate driving signals are transmittedto the AFE inverter to switch a plurality of half bridges included inthe power switches of the AFE inverter.
 19. A method of generating PulseWidth Modulation (PWM) signals for power switches of an Active Front End(AFE) inverter, the method comprising: estimating a synthesized gridvoltage vector angle at a terminal of an alternating current (AC) gridwithout using physical voltage sensors at the terminal of the AC gridby, estimating a terminal voltage of the AFE inverter when the AFEinverter is enabled, the terminal voltage of the AFE inverter being avoltage of a terminal of the AFE inverter, estimating a first AFEinverter terminal voltage vector angle when the AFE inverter isdisabled, the first AFE inverter terminal voltage vector angle being anangle associated with the voltage vector of the terminal of the AFEinverter at an initial time, determining a second AFE inverter terminalvoltage vector angle when the AFE inverter is enabled, the second AFEinverter terminal voltage vector angle being an angle associated withthe voltage vector of the terminal of the AFE inverter at a second timesubsequent to the initial time, and estimating the synthesized gridvoltage vector angle based on the second AFE inverter terminal voltagevector angle, the synthesized grid voltage vector angle being an angleassociated with a voltage vector at the terminal of the AC gridgenerating the PWM signals to control the power switches of the AFEinverter based on at least (i) the synthesized grid voltage vector angleat the terminal of the AC grid and (ii) a AC grid terminal referencepower factor, the AC grid terminal reference power factor representing adesired phase shift between the voltage vector and a current vector atthe terminal of the AC grid; and controlling the AFE inverter to supplypower to a load based on the PWM signals.
 20. (canceled)
 21. The methodof claim 19, wherein the generating the PWM signals comprises:converting measured current from a measured 3-phase current in astationary reference frame to a measured direct-quadrature (dq)-axiscurrent in a dq rotating reference frame; generating a q-axis currentreference based on the AC grid terminal reference power factor;generating a d-axis current reference based on an actual DC bus voltageand a reference DC bus voltage, the actual DC bus voltage beingconnected to the load, the d-axis current reference and the q-axiscurrent reference forming a dq-axis current reference; generatingdq-axis reference voltages based on the measured dq-axis current in thedq rotating reference frame and the dq-axis current reference; andgenerating 3-phase gate driving signals for the AFE inverter byconverting the dq-axis reference voltages based on the synthesized gridvoltage vector angle, the 3-phase gate driving signals being the PWMsignals.
 22. The method of claim 19, wherein the generating the PWMsignals generates the PWM signals such that the AFE inverter maintainsan actual DC bus voltage connected to the load.
 23. A controllercomprising: a memory having computer-readable instructions storedtherein; and a processor configured to execute the computer-readableinstructions to, estimate a synthesized grid voltage vector angle at aterminal of an alternating current (AC) grid without using physicalvoltage sensors at the terminal of the AC grid; generate Pulse WidthModulation (PWM) signals to control power switches of an Active FrontEnd (AFE) inverter based on at least (i) the synthesized grid voltagevector angle at the terminal of the AC grid and (ii) a AC grid terminalreference power factor without using physical voltage sensors at theterminal of the AC grid, the AC grid terminal reference power factorrepresenting a desired phase shift between a voltage vector and acurrent vector at the terminal of the AC grid, wherein the controller isconfigured to generate the PWM signals by, converting measured currentfrom a measured 3-phase current in a stationary reference frame to ameasured direct-quadrature (dq)-axis current in a dq rotating referenceframe, generating a q-axis current reference based on the AC gridterminal reference power factor, generating a d-axis current referencebased on an actual DC bus voltage and a reference DC bus voltage, theactual DC bus voltage being connected to a load, the d-axis currentreference and the q-axis current reference forming a dq-axis currentreference, generating dq-axis reference voltages based on the measureddq-axis current in the dq rotating reference frame and the dq-axiscurrent reference, and generating 3-phase gate driving signals for theAFE inverter by converting the dq-axis reference voltages based on thesynthesized grid voltage vector angle, the 3-phase gate driving signalsbeing the PWM signals; and control the AFE inverter to supply power tothe load based on the PWM signals.